Chapter 3
Using “Enhanced Quantization” to Bound
the Cosmological Constant, (for a Bound-on
Graviton Mass), by Comparing Two Action
Integrals (One Being from General
Relativity) at the Start of Inflation
Andrew Walcott Beckwith
Abstract The first result from 2018 is looking at two action integrals and also a
Lagrangian multiplier as a constraint equation (on cosmological expansion). In
doing so, with Padmanabhan’s version version of an inflaton, we then have a
bound upon the cosmological constant. For the record, this is in fidelity with the
author’s publication, in JHEPGC, entitled “Using ‘Enhanced Quantization’ to
Bound the Cosmological Constant, and Computing Quantum Number n for
Production of 100 Relic Mini Black Holes in a Spherical Region of Emergent
Space-Time” which was in 2018. And was the genesis of the two integral comparison idea. The second result from 2018 is to use the inflaton results and conflate
them with John Klauder’s action principle for a way to have the idea of a potential
well, generalized by Klauder, with a wall of space-time in the pre-Planckian regime
to ask what bounds the cosmological constant prior to inflation, and get an upper
bound on the mass of a graviton. The third result from 2018 and the first cited
reference is a redo of a multiverse version of the Penrose cyclic conformal cosmology to show how this mass of a heavy graviton inconsistent from cycle to cycle. The
fourth result from 2020 is to ask if we can, using an idea from a publication by
Diosi, in the Dice 2018 physics conference use a high energy comparison of Planck
Length, and a De Broglie wavelength, to find out if we can extract from our estimate
of Planck mass a statement as to entropy of the early universe, and the fifth result
from 2020 is to comment upon a comparison of the power of the entropy result so
obtained with the number of e foldings arising in inflation. This last question we
view as essential for answering if there is a foundation of inflation which is linked to
quantum gravity. We wish to avoid the anthropic principle in setting initial
conditions for the massive graviton, which is why we referenced the modification of the Penrose CCC theory in part of our manuscript.
A. W. Beckwith (*)
Physics Department, College of Physics, Chongqing University, Chongqing, People’s Republic
of China
e-mail: abeckwith@uh.edu
© Springer Nature Switzerland AG 2021
B. G. Sidharth et al. (eds.), Fundamental Physics and Physics Education Research,
https://doi.org/10.1007/978-3-030-52923-9_3
21
Using “Enhanced Quantization” to Bound
the Cosmological Constant, (for a Bound-on
Graviton Mass), by Comparing Two Action
Integrals (One Being from General
Relativity) at the Start of Inflation
Andrew Walcott Beckwith
Abstract The first result from 2018 is looking at two action integrals and also a
Lagrangian multiplier as a constraint equation (on cosmological expansion). In
doing so, with Padmanabhan’s version version of an inflaton, we then have a
bound upon the cosmological constant. For the record, this is in fidelity with the
author’s publication, in JHEPGC, entitled “Using ‘Enhanced Quantization’ to
Bound the Cosmological Constant, and Computing Quantum Number n for
Production of 100 Relic Mini Black Holes in a Spherical Region of Emergent
Space-Time” which was in 2018. And was the genesis of the two integral comparison idea. The second result from 2018 is to use the inflaton results and conflate
them with John Klauder’s action principle for a way to have the idea of a potential
well, generalized by Klauder, with a wall of space-time in the pre-Planckian regime
to ask what bounds the cosmological constant prior to inflation, and get an upper
bound on the mass of a graviton. The third result from 2018 and the first cited
reference is a redo of a multiverse version of the Penrose cyclic conformal cosmology to show how this mass of a heavy graviton inconsistent from cycle to cycle. The
fourth result from 2020 is to ask if we can, using an idea from a publication by
Diosi, in the Dice 2018 physics conference use a high energy comparison of Planck
Length, and a De Broglie wavelength, to find out if we can extract from our estimate
of Planck mass a statement as to entropy of the early universe, and the fifth result
from 2020 is to comment upon a comparison of the power of the entropy result so
obtained with the number of e foldings arising in inflation. This last question we
view as essential for answering if there is a foundation of inflation which is linked to
quantum gravity. We wish to avoid the anthropic principle in setting initial
conditions for the massive graviton, which is why we referenced the modification of the Penrose CCC theory in part of our manuscript.
A. W. Beckwith (*)
Physics Department, College of Physics, Chongqing University, Chongqing, People’s Republic
of China
e-mail: abeckwith@uh.edu
© Springer Nature Switzerland AG 2021
B. G. Sidharth et al. (eds.), Fundamental Physics and Physics Education Research,
https://doi.org/10.1007/978-3-030-52923-9_3
21